By using the binomial expansion, or otherwise, express \(( 1 + 2 x ) ^ { 4 }\) in the form
$$1 + a x + b x ^ { 2 } + c x ^ { 3 } + 16 x ^ { 4 }$$
where \(a\), \(b\) and \(c\) are integers.
Hence show that \(( 1 + 2 x ) ^ { 4 } + ( 1 - 2 x ) ^ { 4 } = 2 + 48 x ^ { 2 } + 32 x ^ { 4 }\).
Hence show that the curve with equation
$$y = ( 1 + 2 x ) ^ { 4 } + ( 1 - 2 x ) ^ { 4 }$$
has just one stationary point and state its coordinates.